Bidiagonalization of (k, k + 1)-tridiagonal matrices

Fast block diagonalization of k-tridiagonal matrices

In the present paper, we give a fast algorithm for block diagonalization of k-tridiagonal matrices. The block diagonalization provides us with some useful results: e.g., another derivation of a very recent result on generalized k-Fibonacci numbers in [M.E.A. El-Mikkawy, T. Sogabe, A new family of k-Fibonacci numbers, Appl. Math. Comput. 215 (2010) 4456– 4461]; efficient (symbolic) algorithm for...

The Characteristic Polynomial of Some Perturbed Tridiagonal k-Toeplitz Matrices

We generalize some recent results on the spectra of tridiagonal matrices, providing explicit expressions for the characteristic polynomial of some perturbed tridiagonal k-Toeplitz matrices. The calculation of the eigenvalues (and associated eigenvectors) follows straightforward. Mathematics Subject Classification: 15A18, 42C05, 33C45

Inversion of k-tridiagonal matrices with Toeplitz structure

In this paper, we consider an inverse problem with the k-tridiagonal Toeplitz matrices. A theoretical result is obtained that under certain assumptions the explicit inverse of a ktridiagonal Toeplitz matrix can be derived immediately. Two numerical examples are given to demonstrate the validity of our results. (c) ٢٠١٢ Elsevier Ltd. All rights reserved.

On the coexistence of conference matrices and near resolvable 2-(2k+1, k, k-1) designs

We show that a near resolvable 2-(2k + 1, k, k − 1) design exists if and only if a conference matrix of order 2k+2 does. A known result on conference matrices then allows us to conclude that a near resolvable 2-(2k + 1, k, k − 1) design with even k can only exist if 2k + 1 is the sum of two squares. In particular, neither a near resolvable 2-(21, 10, 9) design nor a near resolvable 2-(33, 16, 1...

Reflection K-Matrices